There are wars that are not wars of aggression

Some wars are just. No war of aggression is just. Therefore, there are wars that are not wars of aggression. Make suggestions for an alternate proof for the two arguments below. Consider the following questions: • If the proof was done using RAA, could it be done using CP? What about vice versa? • Will a direct proof work for any of these? • Can the proof be performed more efficiently by using different equivalence rules? You need not address every one of these questions, but they should serve as a guide to what to look for when offering an evaluation. Argument 1: Some wars are just. No war of aggression is just. Therefore, there are wars that are not wars of aggression. (Wx = x is a war, Jx = x is just, Ax = x is a war of aggression). (?x)(Wx · Jx), (x)(Ax ? ~Jx) ? (?x)(Wx · ~Ax) 1. (?x)(Wx · Jx) 2. (x)(Ax ? ~Jx) ? (?x)(Wx · ~Ax) 3. Ac ? ~Jc 2 UI 4. Wc · Jc 1 EI 5. Wc Assumption for CP 6. Jc 4 Simp 7. ~Ac 3,6 DS 8. Wc · ~Ac 5,7 Conj 9. (?x)(Wx · ~Ax) 8 EG Argument 2: At least one instance of intentional killing is not wrong. But every murder is wrong. Hence, some instances of intentional killing are not murder. (Kx = x is an instance of intentional killing, Wx = x is wrong, Mx = x is murder) Proof using RAA: 1. (?x)(Kx · ~Wx) 2. (x)(Mx ? Wx) ? (?x)(Kx · ~Mx) 3. ~(?x)(Kx · ~Mx) Assume for RAA 4. (x)~(Kx · ~Mx) 3 QN 5. Ka · ~Wa 1 EI 6. ~(Ka · ~Ma) 4 UI 7. ~Ka v ~~Ma 6 DeM 8. ~Ka v Ma 7 DN 9. Ma ? Wa 2 UI 10. ~Wa 5 Simp 11. ~Ma 9, 10 MT 12. ~Ka 8, 11 DS 13. Ka 5 Simp 14. Ka · ~Ka 12, 13 Conj 15. (?x)(Kx · ~Mx) 3-14 RAA